Elastic Settlement in Soil

1CE-632Foundation Analysis and Design

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Design

Settlement of FoundationSettlement of Foundation

Foundation Analysis and Design: Dr. Amit Prashant

SettlementSettlementSettlement

S = Se + Sc + Ss

ImmediateSettlement

Se

PrimaryConsolidation

Sc

SecondaryConsolidation

Ss

2

Immediate Settlement: Occurs immediately after the construction. This is computed using elasticity theory (Important for Granular soil)

Primary Consolidation: Due to gradual dissipation of pore pressure induced by external loading and consequently expulsion of water from the soil mass, hence volume change. (Important for Inorganic clays)

Secondary Consolidation: Occurs at constant effective stress with volume change due to rearrangement of particles. (Important for Organic soils)

For any of the above mentioned settlement calculations, we first need vertical stress increase in soil mass due to net load applied on the foundation


ElasticityElasticity

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2Foundation Analysis and Design: Dr. Amit Prashant

Stress Distribution: Concentrated load Stress Distribution: Concentrated load Boussinesq Analysis

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Stress Distribution: Concentrated load Stress Distribution: Concentrated load Boussinesq Analysis

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Where,


Vertical Stress: Concentrated loadVertical Stress: Concentrated load

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Influence Factor for General solution of vertical stress

2z BP Iz

=0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

BI

r z


Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load

Uniformly Distributed Circular Load

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Vertical Stress: Uniformly Distributed Circular LoadVertical Stress: Uniformly Distributed Circular Load

Rigid Plate on half Space

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Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area

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Vertical Stress: Rectangular AreaVertical Stress: Rectangular Area

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Foundation Analysis and Design: Dr. Amit PrashantPressure BulbPressure BulbSquare Footing Strip Footing

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Pressure Pressure Bulb for Bulb for Square Square FoundationFoundation

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Pressure Pressure Bulb for Bulb for CircularCircularFoundationFoundation

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NewmarksNewmarks ChartChart

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Influence Value

This Model is good for normally-consolidated, lightly overconsolidated clays, and variable deposits


Newmarks ChartNewmarks ChartPoint of stress calculation

Depth = z2

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Determine the depth, z, where you wish to calculate the stress increase

Adopt a scale as shown in the figure Draw the footing to scale and place

the point of interest over the center of the chart

Count the number of elements that fall inside the footing, N

Calculate the stress increase as:

Depth = z1


Westergaards MethodWestergaards Method Provided solution for layered soils Point Loads Assumption:

Elastic soil mass is laterally reinfrced by numorous, closely spaced, horizontal sheets of negligible thickness but infinite rigidity, that allow only vertical movement but prevent the mass as a whole from undergoing any lateral

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p g g ystrain.

( )32

22 2

12zPz C r z

= + ( )

1 22 1

C =

This Model is specially good for pre-compressed or overconsolidated clays


WestergaardsWestergaards influence Chartinfluence Chart

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FrFrhlichhlich Chart with Chart with concentration factor concentration factor m = 4m = 4

( )0.005 .z n q =

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This Model is specially good for Sands


Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)

1.52

1 1 ( )2z zDB qz

= +

Circular Foundation:

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Square Foundation:

1.762

1 1 ( )2z zDf

B qz

= +


Simplified Methods (Simplified Methods (Poulos and Davis, 1974)Poulos and Davis, 1974)

Strip Foundation:

2.602

1 1 ( )2z zDf

B qz

= +

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Rectangular Foundation:

( )2.60 0.84 /1.38 0.62 /1 1 ( )

2

B LB L

z zDf

B qz

+ = +


Approximate Approximate MethodsMethods

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( ) ( )..z

B LqB z L z

= + +

( )2

2zBq

B z = +

( )zBq

B z = +

Rectangular Foundation:

Square/Circular Foundation:

Strip Foundation:


Contact Pressure and Settlement distributionContact Pressure and Settlement distribution

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Cohesive Soil - Flexible Footing

Cohesive Soil - Rigid Footing

Granular Soil Flexible Footing

Granular Soil - Rigid Footing


Elastic settlement of FoundationElastic settlement of Foundation

( )0 0

1H He z z s x s y

s

S dz dzE

= = sE = Modulus of elasticity

H = Thickness of soil layers = Poissons ratio of soil

Elastic settlement:

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sElastic settlement for Flexible Foundation:

( )21e s fs

qBS IE

=

fI = influence factor: depends on the rigidity and shape of the foundation

sE = Avg elasticity modulus of the soil for (4B) depth below foundn level



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E in kPa

25



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Elastic settlement of FoundationElastic settlement of FoundationSoil Strata with Semi-infinite depth

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Steinbrenners Influence Factors for Settlement of the Corners of Steinbrenners Influence Factors for Settlement of the Corners of loaded Area loaded Area LxBLxB on Compressible Stratus of on Compressible Stratus of = 0.5= 0.5, and Thickness , and Thickness HHtt

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Strain Influence Factor Method for Sandy Soil: Strain Influence Factor Method for Sandy Soil: SchmertmannSchmertmannand Hartman (1978)and Hartman (1978)

( ) 21 20

zz

e fs

IS C C q D zE

= 1C = Correction factor for foundation depth( ){ }1 0.5 f fD q D 2C = Correction factor for creep effects

q For square and circular foundation:

( )1 0.2 log time in years 0.1 +

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q

For foundation with L/B >10:

Interpolate the values for 1 < L/B < 10


ExampleExample

( ) 21 20

zz

e fs

IS C C q D zE

= 231.39fD kN m =

For square and circular foundations

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3.5s cE q

2.5s cE qFor rectangular

foundations

800 in kPasE N Correlation with SPT data:

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Burland and Burbidges Method for Sandy SoilsBurland and Burbidges Method for Sandy Soils

Depth of Stress Influence (z'):

( )0.751.04 ,where B is in metersz B =If N60' is constant or increasing with depth, then If N60' is decreasing with depth, use smaller of

( ) 21 25 L B Elastic Settlement (Se): where B is in meters2 and Thickness of soft layer below foundationz B z z = = =

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( )( )1 2 3

1.250.25e

L BS Bq

L B = +

where B is in meters and is in kPaq

1 = 0.0047 for NC sand0.0016 for OC sand with qna po0.0047 for OC sand with qna po

( )( )

1.42

1.4

1.71

0.57

N

N

==

Compressibility Index: for NC sand

for OC sand

3 2 1z zz z

= for NC sand and for OC sand with qna po

for OC sand with qna po0.67na oq q p = naq q =


Settlement due to Primary ConsolidationSettlement due to Primary Consolidation

log log1 1

s c c c c o avc

o o o c

C H C HSe e

+ = + + +

log1

s c o avc

o o

C HSe

+ = +

log1

c c o avc

o o

C HSe

+ = + For NC clay

For OC clay ( )o av c +

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Elastic Settlement in Soil